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This paper deals with the problem of local ambiguity function shaping in the presence of narrow-band spectral interferences (e.g., the communication signal and jamming), which has significant applications in the radar detection field. An objective function involving the weighted integrated sidelobe level and the spectral stopband energy is developed as a figure of merit to minimize. Besides, the energy and the peak-to-average ratio restrictions are forced on the probing waveform. To handle the resulting non-convex quartic optimization problem, an iterative sequential quartic optimization algorithm sharing polynomial time complexity is proposed. In each iteration, it decomposes the original problem into two alternately tractable quadratic subproblems both of which can be converted to linear optimization problems with closed-form solutions. Finally, the numerical simulations are provided to assess the effectiveness of the proposed algorithm. The results show that the proposed algorithm outperforms some available counterparts in the aspect of the convergence speed and the capability to prohibit the narrow-band spectral interferences and the sidelobes of a strong return from masking weak targets.

Cognitive Local Ambiguity Function Shaping With Spectral Coexistence